They do look good, but nope, wasn't just for style. There is a HUGE difference in carrying, mounting, swinging, and holding on target between a swamped barrel and a straight or straight-tapered barrel. I speak from experience.
I have two longrifles. One is a Traditions Pennsylvania Longrifle from about 2003 or 2004 when they came with a 40¼" straight barrel. The other is an Early Lancaster with a 44½" swamped barrel. The straight barrel and all BP Octagon straight barrels are nose heavy. The significantly longer Early Lancaster rifle seen in my avatar (with the butt resting on the ground) is perfectly balanced to the point where I normally hold onto the forearm with my left hand. It's far easier to carry, mount, swing, and hold on target than the straight barreled and shorter Traditions longrifle - no comparison. My much longer Early Lancaster is almost 2-lbs lighter than the Traditions too.
The barrels in the 1700's and all rifled barrels until Remington developed their method to drill out steal blanks in about 1838, were all hammer forge-welded by hand out of a flat skelp of iron. If the gunsmith making the barrel wanted the muzzle to be thinner, he could have kept moving the iron with his hammer like blacksmiths always do. That doesn't mean that someone didn't accidentally do it that way once upon a time or just leave it thicker because they didn't want to hammer any more; but the Moravians in Germany had been making rifles with swamped barrels since the 1600's and the gunsmiths who migrated to America were some of those Moravians who had previously been building Jaeger rifles in some of the German provinces. Those Jaeger rifles were much shorter than the American Longrifles and also fired a larger lead ball. Over time, those Jaeger rifles evolved into the longer, smaller caliber American Longrifle. So in America, building a a swamped barrel was already common practice by the gunsmiths moving here from Germany.
Here's an example of a Jeager rifle:
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Here's a shot of my Early Lancaster American Longrifle.(with a swamped barrel). Balance is superb resulting in exceptional handling.:
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And here's a Traditions Pennsylvania Longrifle, which is shorter, much bulkier, has a straight barrel and is heavier than my Early Lancaster rifle above. As with all straight or straight-tapered barrels it is nose-heavy. It also has an adjustable rear sight which was not available in the 18th century.
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Prior to Remington inventing a long, hollow, drill bit to drill through steel blanks, drill bits never lasted very long when attempting to drill steel blanks. Drilling those steel blanks generated too much heat and would anneal the bit ruining it before the blank was a usable length. With the hollow drill bit though, Remington could (and did) continually feed cutting oil to the the tip of the bit to keep it cutting without generating too much heat. Barrels also got a lot shorter when they did that and half-stock guns became the norm.
Here's a shot of a Hawken percussion cap rifle from the Cody Museum's collection:
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That drilled barrel dropped the construction time for a barrel down from perhaps a week of hand-hammering to make one barrel to just hours or perhaps a day to make one. It also allowed for accurate and repeatable calibers whereas with the hammer forge-welded barrels you could end up with many different calibers from folding that skelp around the same mandrel and then reaming it out to make sure it was straight before rifling it. These variances were so unique to each gun that the price of a new rifle included the bag mold to make the correct size lead ball to fit it. Using that long, hollow drill bit to drill it out also eliminated the need for a mandrel to build it around, or reaming out the barrel before rifling it. .50-caliber barrels were always .50 caliber. Prior to that it might have come out anywhere from about .49 caliber to .54 caliber using the same mandrel to build the barrels around.